If a person is born outside the US to a US citizen father and a non-US national mother, and the parents are not married to each other, then there are certain special requirements in order for the child to be a US citizen. Under 8 USC §1409(a)(3), one of the requirements is that the father must agree in writing to provide financial support for the child until they reach the age of 18. If all the conditions of 8 USC §1409(a) are met, then 8 USC §1401(g) applies "as of the date of birth" of the person, i.e., they are considered a US citizen from birth.
Thus, the person's citizenship is conditional upon a particular act that must be performed before they reach the age of 18. As long as the father has written down somewhere, prior to the child's 18th birthday, that they agree to support the child financially until the age of 18 (or even just signed such an agreement written by someone else), this condition is fulfilled and the child is a citizen if all other conditions are met. If the child is over the age of 18 but has such a document in their possession that is dated before their 18th birthday, they can use it to prove that the condition was met and that they are a US citizen. However, if by the time the child turns 18 the father is still alive but has never made such a written agreement, then the child is not a US citizen.
There are two ways to interpret the law:
It grants citizenship. If, at some point between the child's birth and the child's 18th birthday, all the conditions of 8 USC §1409(a) are fulfilled, then the law grants citizenship to such child, and this grant is retroactive to their birth. (This interpretation raises the constitutional question of whether such a citizen would be eligible for the presidency.)
It takes away citizenship. The child is born a citizen, but if the child reaches the age of 18 and the conditions have not been met, their citizenship is taken away by operation of law. It is constitutional for Congress to provide for the loss of citizenship of individuals who were born outside the US and not naturalized in the US. See Rogers v. Bellei. However, this interpretation seems less likely to me. I would normally think that if Congress had intended to write a law that takes away citizenship, they would be a bit more explicit about it. Furthermore, it seems unlikely that a person who is still under the age of 18 and for whom the condition still could be met in the future could claim current US citizenship in e.g. removal proceedings.
Which interpretation is correct?